Asymptotics for Voronoi tessellations on random samples

DOI10.1016/S0304-4149(99)00035-6zbMath0999.60007OpenAlexW2081107648MaRDI QIDQ1613642

K. McGivney, Joseph E. Yukich

Publication date: 29 August 2002

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0304-4149(99)00035-6

zbMATH Keywords

complete convergencestochastic geometryVoronoi tessellationtotal edge length

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05)

Related Items (9)

Weak laws of large numbers in geometric probability ⋮ Strong laws for Euclidean graphs with general edge weights ⋮ Normal approximation in total variation for statistics in geometric probability ⋮ Limit theory for unbiased and consistent estimators of statistics of random tessellations ⋮ Surface order scaling in stochastic geometry ⋮ Gaussian limits for random measures in geometric probability ⋮ Asymptotic theory for statistics of the Poisson-Voronoi approximation ⋮ Palm theory, random measures and Stein couplings ⋮ On the choice of weight functions for linear representations of persistence diagrams

Cites Work

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• On central limit theorems in geometrical probability
• Lectures on random Voronoi tessellations
• Limit theorems and rates of convergence for Euclidean functionals
• Probability theory of classical Euclidean optimization problems
• Concentration of measure and isoperimetric inequalities in product spaces
• Asymptotics for Euclidean functionals with power-weighted edges
• Weighted sums of certain dependent random variables
• On the homogeneous planar Poisson point process
• On the size of a random sphere of influence graph

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